A Multiplexed Model Predictive Control (MMPC) scheme with Quadratic Dissipativity Constraint (QDC) for interconnected systems is presented in this paper. A centralized MMPC is designed for the global system, wherein the controls of subsystems are updated sequentially to reduce the computational time. In MMPC, the global state vector of the interconnected system is required by the optimization. The QDC is converted into an enforced stability constraint for the MMPC as an alternative to the terminal constraint and terminal cost in this approach. The nominal recursive feasibility for the global system and the iterative feasibility for the local subsystems are obtained via set operations on the invariant sets. The admissible sets for the control inputs are obtained and employed in this approach for the QDC-based stability constraint. The set operations are speed up by multiple magnitudes thanks to the implementation of multiplexed inputs in MMPC. Numerical simulations with Automatic Generation Control (AGC) in power systems having tie-lines demonstrate the theoretical development.